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hw2 - Home assignment N2 Tensile Strength(lb/in*in yij 3129...

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Home assignment N2. MixTech, i Tensile Strength (lb/in*in), ij y 1 3129 3000 2865 2890 2 3200 3300 2975 3150 3 2800 2900 2985 3050 4 2600 2700 2600 2765 N of Techniques: 4 a = N of Experiments : 4 n = N of Observations 16 N an = = Problem 3.1 a). Test the hypothesis that mixing techniques affects the strength of the cement. Use 0,05 α = . MixTech, i Totals, i y Averages, . i y 1 11884 2971 2 12625 3156,25 3 11735 2933,75 4 10665 2666,25 .. 46909 y = .. 2931,81 y = 2 2 .. 1 1 643648,44 a n T ij i j y SS y N = = = - = ∑∑ 2 2 .. . 1 489740,18 a Treatment i j y SS y N = = - = 153908,25 E T Treatment SS SS SS = - = Source of Variation Sum of Sq. Deg.of Fr. Mean Sq. Fo P-Value Tech 489740,19 3 163246,73 12,728107 0,0004887 Error 153908,25 12 12825,688 Total 643648,44 15 Since P-Value<5%, we reject the hypothesis H 0 . It means that the technique affects the strength. c). Use the Fisher LSD method with 0,05 α = to make comparisons between pairs of means.
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LSD-test, . . i j y y - 2 3 4 1 -185,25 37,25 304,75 2 222,5 490 3 267,5 /2, 0,025 2 2 * 174,5 E E N MS MS LSD t t n n α α - = = = . (We compare this value with the values in the table.) Thus, all techniques, except 1 and 3, have a significantly different effect.
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